In a medium bowl, beat the eggs with the ham. Season with salt and plenty of pepper. In a large nonstick skillet, heat 3 tablespoons of oil over high heat until shimmering. Pour in the egg mixture, evenly distributing the ham. Using a spatula, lift the cooked edges, tilting the pan so the uncooked eggs seep underneath. If the omelet sticks, drizzle a little more oil around the edge. Lower the heat to moderate and cook until the omelet is golden on the bottom and the top is almost completely set, 2 to 3 minutes. Fold the omelet in thirds and slide it onto a platter.